Question

if a+ib=(x+i)^2/2x-i prove that a^2+b^2= (x^2+1)^2/4x^2+1​

Answer 1

Answer:

Proof in explanation

Step-by-step explanation:

a + ib = (x + i)² / (2x - i)

∴ a - ib = (x - i)² / (2x + i)

∴ (a + ib) (a - ib) = [(x + i)² / (2x - i)] * [(x - i)² / (2x + i)]

∵ (a + ib) (a - ib) = a² + b²

a² + b² = [(x + i)² * (x - i)² ] / [(2x - i) * (2x + i)]

           = [(x + i)*(x - i)]² / (4x² + 1)

           = [x² + 1]² / (4x² + 1)

           = RHS